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7. Atmospheric neutrinos and
Neutrino oscillations
Corso “Astrofisica delle particelle”
Prof. Maurizio SpurioUniversità di Bologna. A.a.
2011/12
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Outlook Some history Neutrino Oscillations How do we search for neutrino
oscillations Atmospheric neutrinos 10 years of Super-Kamiokande Upgoing muons and MACRO Interpretation in terms on neutrino
oscillations Appendix: The Cherenkov light
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At the beginning of the ’80s, some theories (GUT) predicted the proton decay with measurable livetime
The proton was thought to decay in (for instance) pe+p0ne
Detector size: 103 m3, and mass 1kt (=1031 p) The main background for the detection of proton
decay were atmospheric neutrinos interacting inside the experiment
7.1 Some history
Proton decay
gg
e Neutrino Interaction
Water Cerenkov Experiments (IMB, Kamiokande)
Tracking calorimeters (NUSEX, Frejus, KGF)
Result: NO p decay ! But some anomalies on the neutrino measurement!
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7.2 Neutrino Oscillations
|ne , |nm , |nt =Weak Interactions (WI) eigenstats
|n1 , |n2 , |n3 =Mass (Hamiltonian) eigenstats
Idea of neutrinos being massive was first suggested by B. Pontecorvo
Prediction came from proposal of neutrino oscillations
• Neutrinos propagate as a superposition of mass eigenstates
Neutrinos are created or annihilated as W.I. eigenstates
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Weak eigenstates (ne, nm, nt) are expressed as a combinations of the mass eigenstates (n1, n2,n3).
These propagate with different frequencies due to their different masses, and different phases develop with distance travelled. Let us assume two neutrino flavors only.
The time propagation: |n(t)= (|n1 , |n2 )
02
222
ij
iiii
ME
mEmpMn
n
M = (2x2 matrix)
(eq.2)
)(tMdt
di n
n (eq.1)
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eq.1 becames, using eq.2)
)(2
2
tvE
mEdt
di i
nn
n
whose solution is :ti
iiievtv )0()(
nn
EmE i
i 2
2
with
During propagation, the phase difference is:
nEtmm
i 2)( 2
122
(eq.4)
(eq.6)
(eq.5)
Time propagation
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|ne = cosq |n1 + sinq |n2
|nm = -sinq |n1 + cosq |n2
q = mixing angle
(eq.3)
Time evolution of the “physical” neutrino states:
• Let us assume two neutrino flavors only (i.e. the electon and the muon neutrinos).
• They are linear superposition of the n1,n2 eigenstaten:
titi
titie
i
i
evevv
evevv21
21
)0(cos)0(sin
)0(sin)0(cos
21
21
m
(eq.7)
• Using eq. 5 in eq. 3, we get:
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• At t=0, eq. 7 becomes:
)0(cos)0(sin
)0(sin)0(cos
21
21
vvv
vvve
m
)0(cos)0(sin)0(
)0(sin)0(cos)0(
2
1
m
m
vvv
vvv
e
e
• By inversion of eq. 8:
(eq.8)
• For the experimental point of view (accelerators, reactors), a pure muon (or electron) state a t=0 can be prepared. For a pure nm beam, eq. 9:
)0(cos)0(
)0(sin)0(
2
1
m
m
q
q
vv
vv
(eq.9)
(eq.10)
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The time evolution of the nm state of eq. 8:titi ievevv 21 )0(cos)0(sin 22
m
mm qq
By definition, the probability that the state at a given time is a nm is:
20 tP mmnn nnmm
(eq. 12)• Using eq. 11, the probability:
titi
t
ee
P)()(22
4420
2121cossin
cossin
mmnn
qqnnmm
2
)(sin2sin1 2122 tP qmmnn
i.e. using trigonometry rules:
(eq.11)
(eq. 13)
(eq. 14)
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nn
EmE i
i 2
2
Finally, using eq.5:
nnn qmm E
tmmP4
)(sin2sin121
2222
With the following substitutions in eq.15:- the neutrino path length L=ct (in Km)- the mass difference m2 = m2
2 – m12
(in eV2)- the neutrino Energy En (in GeV)
nnn qmm E
LmP
222 27.1sin2sin1
To see “oscillations” pattern: 2
27.1
02 p
q
n
ELm
(eq. 15)
(eq. 16)
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7.3 How do we search
for neutrino oscillatio
ns?
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..with atmospheric neutrinos
nnn qmm E
LmP
222 27.1sin2sin1
• m2, sin22Q from Nature;
• En = experimental parameter (energy distribution of neutrino giving a particular configuration of events)
• L = experimental parameter (neutrino path length from production to interaction)
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Appearance/
Disappearance
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nnn qmm E
LmP
222 27.1sin2sin1
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7.4- Atmospheric neutrinos
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The recipes for the evaluation of the atmospheric neutrino
flux-
ee nnm
nmp
m
m
\
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E-3 spectrum
GZK cut
1015 < E< 1018 eVgalactic ?
E < 1015 eVGalactic
E 5. 1019 eVExtra-Galactic?Unexpected?
5. 1019 < E< 3. 1020 eV
i) The primary spectrum
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ii)- CR-air cross section
pp Cross section versus center of mass energy.
Average number of charged hadrons produced in pp (andpp) collisions versus center of mass energy
It needs a model of nucleus-nucleus interactions
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iii) Model of the atmosphere
ATMOSPHERIC NEUTRINO PRODUCTION: • high precision 3D calculations,• refined geomagnetic cut-off treatment (also
geomagnetic field in atmosphere)• elevation models of the Earth• different atmospheric profiles• geometry of detector effects
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Output: the neutrino (ne,nm) flux
See for instance the FLUKA MC: http://www.mi.infn.it/~battist/neutrino.html
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iv) The Detector responseFully Contained
n Partially Contained
Energy spectrum of n for each event categoryn
m
Through going mStopping m
n
m
n
m
Energy spectrum (from Monte Carlo) of atmospheric neutrinos seen with different event topologies (SuperKamiokande)
up-stop m up-thru m
nnn qmm E
LmP
222 27.1sin2sin1
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Rough estimate: how many ‘Contained events’ in 1 kton
detector
1. Flux: n ~ 1 cm-2 s-1
2. Cross section (@ 1GeV): sn~0.5 10-38 cm2
3. Targets M= 6 1032 (nucleons/kton)4. Time t= 3.1 107 s/y
Nint = n (cm-2 s-1) x sn (cm2)x M (nuc/kton) x t (s/y) ~ ~ 100 interactions/ (kton y)
nm
ne
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7.5 10 years of Super-Kamiokande1996.4 Start data taking
1999.6 K2K started
2001.7 data taking was stopped for detector upgrade2001.11 Accident
partial reconstruction2002.10 data taking was resumed
2005.10 data taking stopped for full reconstruction
2006.7 data taking was resumed
2001 Evidence of solar n oscillation (SNO+SK)
1998 Evidence of atmospheric n oscillation (SK)
2005 Confirm n oscillation by accelerator n (K2K)
SK-I
SK-II
SK-III
SK-IV 2009 data taking
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Measurement of contained events and
SuperKamiokande (Japan)
1000 m Deep Underground
50.000 ton of Ultra-Pure Water
11000 +2000 PMTs
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As a charged particle travels, it disrupts the local electromagnetic field (EM) in a medium.
Electrons in the atoms of the medium will be displaced and polarized by the passing EM field of a charged particle.
Photons are emitted as an insulator's electrons restore themselves to equilibrium after the disruption has passed.
In a conductor, the EM disruption can be restored without emitting a photon.
In normal circumstances, these photons destructively interfere with each other and no radiation is detected.
However, when the disruption travels faster than light is propagating through the medium, the photons constructively interfere and intensify the observed Cerenkov radiation.
Cherenkov Radiation
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Cherenkov Radiation
One of the 13000 PMTs of
SK
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How to tell a nm from a ne : Pattern recognition
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nm
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ne
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e or m
Fully Contained (FC)
m
No hit in Outer Detector One cluster in Outer Detector
Partially Contained (PC)
Reduction
Automatic ring fitterParticle IDEnergy reconstruction
Fiducial volume (>2m from wall, 22 ktons) Evis > 30 MeV (FC), > 3000 p.e. (~350 MeV) (PC)
Fully Contained8.2 events/dayEvis<1.33 GeV : Sub-GeVEvis>1.33 GeV : Multi-GeV
Partially Contained0.58 events/day
Contained event in SuperKamiokande
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Contained events. The
up/down symmetry in SK and nm/ne ratio.
Up/Down asymmetry interpreted as neutrino oscillations
Expectations: events inside the detector. For En > a few GeV,Upward / downward = 1
En=0.5GeV En=3 GeV En=20 GeV
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Zenith angle
distributionSK:1289 days
(79.3 kty)
m /eDATA
m /e M C= 0.638 0.017 0.050
Data
• Electron neutrinos = DATA and MC (almost) OK!
• Muon neutrinos = Large deficit of DATA w.r.t. MC !
Zenith angle distributions for e-like and µ-like contained atmosphericneutrino events in SK. The lines show the best fits with (red) and without (blue) oscillations; the best-fit is m2 = 2.0 × 10−3 eV2 and sin2 2θ = 1.00.
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Zenith Angle Distributions (SK-I + SK-II)nm–nt oscillation (best fit)
null oscillation
m-likee-like
P<400MeV/c
P>400MeV/c
P<400MeV/c
P>400MeV/c
NOTE: All topologies, last results (September 2007)
Livetime• SK-I 1489d (FCPC) 1646d (Upmu)• SK-II 804d (FCPC) 828d(Upmu)
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Main features of Macro as n detector
• Large acceptance (~10000 m2sr for an isotropic flux)
• Low downgoing m rate (~10-6 of the surface rate )
• ~600 tons of liquid scintillator to measure T.O.F. (time resolution ~500psec)
• ~20000 m2 of streamer tubes (3cm cells) for tracking (angular resolution < 1° )
More details in Nucl. Inst. and Meth. A324 (1993) 337.
7.6 Upgoing muons and MACRO (Italy)
R.I.P December 2000
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The Gran Sasso National Labs
http://www.lngs.infn.it/
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Up stopIn down
1) 2) 3) 4)
Neutrino event topologies in MACRO
In upUp throughgoing
AbsorberStreamerScintillator
• Liquid scintillator counters, (3 planes) for the measurement of time and dE/dx.
• Streamer tubes (14 planes), for the measurement of the track position;
• Detector mass: 5.3 kton• Atmospheric muon
neutrinos produce upward going muons
• Downward going muons ~ 106 upward going muons
• Different neutrino topologies
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Energy spectra of nm events in MACRO
• <E>~ 50 GeV throughgoing m
• <E>~ 5 GeV, Internal Upgoing (IU) m;
• <E>~ 4 GeV , internal downgoing (ID) m and for upgoing stopping (UGS) m;
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+1 m-1 m
T1
T2Streamer tube track
Neutrino induced events are upward throughgoing muons, Identified by the time-of-flight method
Atmospheric m: downgoing
m from n: upgoing
LcTT 211
LcTT 211
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MACRO Results: event deficit and distortion of the angular
distribution
Observed= 809 eventsExpected= 1122 events (Bartol)Observed/Expected= 0.721±0.050(stat+sys)
±0.12(th)
- - - - No oscillations____ Best fit m2= 2.2x10-3 eV2
sin22q=1.00
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MACRO Partially contained events
consistent with up throughgoing muon results
Obs. 262 eventsExp. 375 eventsObs./Exp. = 0.70±0.19)
Obs. 154 eventsExp. 285 eventsObs./Exp. = 0.54±0.15
IU
ID+UGS
MC with oscillations
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underground detector
Effects of nm oscillations on upgoing events
n
Earth
m
nnn qmm E
LmP
222 27.1sin2sin1
q
• If q is the zenith angle and D= Earth diameter
L=Dcosq• For throughgoing neutrino-induced
muons in MACRO, En = 50 GeV (from Monte Carlo)
q cos(q) m2=0.0002 m2=0.00010 -1,000 0,62 0,89
-10 -0,985 0,63 0,90-20 -0,940 0,66 0,91-30 -0,866 0,71 0,92-40 -0,766 0,77 0,94-50 -0,643 0,83 0,96-60 -0,500 0,89 0,97-70 -0,342 0,95 0,99-80 -0,174 0,99 1,00-90 0,000 1,00 1,00
0,00
0,10
0,20
0,30
0,40
0,50
0,60
0,70
0,80
0,90
1,00
-1,00 -0,80 -0,60 -0,40 -0,20 0,00
cosq
mmnnP
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Oscillation Parameters• The value of the “oscillation parameters” sin2q and m2 correspond to the values which provide the best fit to the data
• Different experiments different values of sin2q and m2
• The experimental data have an associated error. All the values of (sin2q, m2) which are compatible with the experimental data are “allowed”.
• The “allowed” values span a region in the parameter space of (sin2q, m2)
nnn qmm E
LmP
222 27.1sin2sin1
1.9 x 10-3 eV2 < m2 < 3.1 x 10-3 eV2
sin2 2q > 0.93 (90% CL)
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“Allowed” parameters region
90% C. L. allowed regions for νm → νt oscillations of atmospheric neutrinos for Kamiokande, SuperK, Soudan-2 and MACRO.
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Why not νμνe ?
Apollonio et al., CHOOZ Coll.,Phys.Lett.B466,415
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nm disappearance: History Anomaly in
R=(m/e)observed/(m/e)predicted Kamiokande: PLB 1988, 1992 Discrepancies in various
experiments Kamiokande: Zenith-angle
distribution Kamiokande: PLB 1994
Super-Kamiokande/MACRO: Discovery of nm oscillation in 1998 Super-Kamiokande: PRL 1998 MACRO, PRL 1998
K2K: First accelerator-based long baseline experiment: 1999 – 2004 Confirmed atmospheric neutrino results Final result 4.3s: PRL 2005, PRD
2006 MINOS: Precision
measurement: 2005 - First result: PRL2006
Kajita: Neutrino 98
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See for review: The “Neutrino Industry”
http://www.hep.anl.gov/ndk/hypertext/ Janet Conrad web pages:
http://www.nevis.columbia.edu/~conrad/nupage.html
Fermilab and KEK “Neutrino Summer School” http://projects.fnal.gov/nuss/
Torino web Pages: http://www.nu.to.infn.it/Neutrino_Lectures
/
Progress in the physics of massive neutrinos, hep-ph/0308123
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Appendice:La radiazione Cerenkov
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Effetto CerenkovPer una trattazione classica dell’effetto Cerenkov:Jackson : Classical Electrodynamics, cap 13 e par. 13.4 e 13.5La radiazione Cerenkov e’ emessa ogniqualvolta una particella carica attraversa un mezzo (dielettrico) con velocita’ c=v>c/n, dove v e’ la velocita’ della particella e n l’indice di rifrazione del mezzo.Intuitivamente: la particella incidente polarizza il dielettrico gli atomi diventano dei dipoli. Se >1/n momento di dipolo elettrico emissione di radiazione.
<1/n 1/n
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L’ angolo di emissione qc puo’ essere interpretato qualitativamente come un’onda d’urto come succede per una barca od un aereo supersonico.
Esiste una velocita’ di soglia s = 1/n qc ~ 0 Esiste un angolo massimo qmax= arcos(1/n) La cos(q) =1/n e’ valida solo per un radiatore infinito, e’ comunque una buona approssimazione ogniqualvolta il radiatore e’ lungo L>>l essendo l la lunghezza d’onda della luce emessa
lpart=ct
llight=(c/n)tq
wave front
1)(with1cos l
q nnnC
qC
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Numero di fotoni emessi per unita’ di percorso e intervallo unitario di lunghezza d’onda. Osserviamo che decresce al crescere della l
.with 1
sin2112
2
2
2
22
2
222
22
constdxdE
NdEhcc
dxdNd
zn
zdxd
NdC
nl
ll
qlp
lp
l
dN/dl
l
dN/dE
Il numero di fotoni emessi per unita’ di percorso non dipende dalla frequenza
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L’ energia persa per radiazione Cerenkov cresce con . Comunque anche con 1 e’ molto piccola.Molto piu’ piccola di quella persa per collisione (Bethe Block), al massimo 1% .
dnc
zdxdE
22
2 11
medium n qmax (=1) Nph (eV-1 cm-1)
air 1.000283 1.36 0.208isobutane 1.00127 2.89 0.941water 1.33 41.2 160.8quartz 1.46 46.7 196.4
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1) Esiste una soglia per emissione di luce Cerenkov
2) La luce e’ emessa ad un angolo particolareFacile utilizzare l’effetto Cerenkov per identificare le particelle. Con 1) posso sfruttare la soglia Cerenkov a soglia. Con 2) misurare l’angolo DISC, RICH etc.La luce emessa e rivelabile e’ poca.Consideriamo un radiatore spesso 1 cm un angolo qc = 30o ed un E = 1 eV ed una particella di carica 1. 5.9225.0370sin370
sin
2
22
ELNc
zdEdxdN
cph
c
Considerando inoltre che l’efficienza quantica di un fotomoltiplicatore e’ ~20% Npe=18 fluttuazioni alla Poisson